Still running on Broadway after nearly six years and 3,400 performances, the musical Mary Poppins could and ought not care less about criticism of any sort. As a willful entertainment machine, it is well-greased and works overtime, and the results are undeniably impressive, if somewhat more grim than charming. It may be hard to imagine a better job translating the movie to the stage. The book deftly expands the drama to flesh out the dilemmas of the Banks parents, adding dimension to the stakes at issue. So, too, the music has been adapted to provide an element of operetta-like continuity to the performance, and the new songs (save for a relatively weak climactic number, the generic “Anything Can Happen”) seamlessly create more opportunities for successful dance and production numbers.

There is an extraordinary amount of expertise visible onstage, strikingly marshaled by original director Richard Eyre and choreographer/co-director Matthew Bourne. Bob Crowley’s scenic and costume design amply deserved their Tony award, and the feeling of being in such crack hands makes the naked manipulation go down with, so to speak, a spoonful of sugar. The touring company boasts an especially strong and well-drilled ensemble, with plenty of real dancing and stentorian choral work. The show looks plenty expensive and disguises the threadbare story with relentless pizzazz.

Of course, it is manifestly unfair to have to follow Julie Andrews and Dick van Dyke. Rachel Wallace’s governess is more steely, with the impassive smiling mask of the trouper standing in for the nanny’s confident poise, her gestures so tightly broken into contained gesticulations that they become their own starchy kabuki, far more Eleanor Powell or Jessie Matthews than the inimitable Miss Andrews. Bert has the benefit of being a far better realized character than in the film, playing the ringmaster for the action, and Nicolas Dromard, despite the far too blatant dancing-on-the-ceiling bit, actually conjures up welcome memories of some of James Cagney’s steps.

The father, who is learning to be less of a grownup, and the haplessly frustrated mother, who left the stage for domestic life, become the most sympathetic characters, for whom we fear more than for the children. Elizabeth Broadhurst, despite having played the mother more than 1,000 times on the road, remains fresh and vibrant, and Michael Dean Morgan resists the clichés of Mr. Banks by dint of being capable of playing broad without forfeiting restraint. Q. Smith, assaying both the woman who feeds the birds and the holy terror of Mr. Banks’ original nanny, gives outsized bravura a good shaking with vocal pyrotechnics and pathos.

On a negative note, the Ahmanson amplification system, while amply loud, tended toward the muddy and obscured some of the lines, notwithstanding the excellent diction. This had not been a problem with either of the previous Ahmanson shows (“Follies” and “War Horse”), so perhaps the demands of the production had difficulty with the hall’s infamously unresponsive acoustics. And a word to toddlers and small children, especially at matinees: do instruct your parents that it is distracting to chatter incessantly while the performers are doing their very best right there in front of you, unlike at home in front of the television.